Woolmer, 58, was found unconscious in his hotel room in Jamaica and died less than an hour later.
The paper said that the local police are investigating whether he died of an accidental overdose.
Pakistan team officials revealed he was diabetic and had breathing problems in his sleep.
Woolmer's wife Gill and sons Dale, 27 and Russell, 24, were told of his death at their home in South Africa last night.
According to the paper Gill said her husband had been depressed over Pakistan's shock defeat by Ireland on Saturday. "His job coaching there has been incredibly stressful," she said.
The paper, however reported, that a friend said Woolmer told him a few days ago: "Don't worry about me mate, I'm the last person to die of a heart attack, I've seen it all."
In 1999 was approached for the England job but turned it down, saying he need a rest after the stress of coaching South Africa.
Kent all-rounder Woolmer played 19 Test matches for England between 1975 and 1981. Retired umpire Dickie Bird said: "His death is a great tragedy. I'm stunned."